Puzzle – Degrees between Hand of Clocks on 3:15

Puzzle: What is the angle between the hour hand and the minute hand on a clock if the time is 3:15?

Angle Between Hour and Minute hand when time is 3:15

Solution:
This type of problem, to find the angle between the hour hand and the minute hand, can be solved using the following steps.

• Find the angle made by the minute hand with the 12 o’clock position.
• Find the angle made by the hour hand with the 12 o’clock position.
• Calculate the difference between these two angles, which is the angle between the hour hand and minute hand.

Step 1: Calculate the angles by considering the 12 O’clock position as a reference.

• Angle made by minute hand: minute hand completes one rotation in one hour i.e 60 minutes.
  So in one minute, it moves by 360/60 = 6°.
• Angle made by Hour hand: hour hand completes one rotation in 12 hours. i.e 720 minutes.
  So it moves by 360/12 = 30° in one hour and 360/720 = 0.5° in one minute.

In H hours and M minutes, with respect to the 12 o’clock position the angle made by the minute hand = M×6° and the angle made by the hour hand = (H×30 + M×0.5)°.

Step 2 (degrees at 3:15):

At 3:15 in the clock, H = 3 and M = 15.
Angle made by minute hand = M×6° = 15×6° = 90°
Angle made by hour hand = (H×30 + M×0.5)° = (3×30 + 15×0.5) ° = 97.5°
Angle between hour hand and minute hand = 97.5° – 90° = 7.5°

Degree difference at 3:15

The angle between the hour hand and the minute hand on a clock at 3:15 is 7.5°